A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L1, L2, L3, L4, L5, L6. The generator bus G1 is considered as slack bus, and the load buses L3 and L4 are voltage controlled buses. The generator at bus G2 cannot supply the required reactive power demand, and hence it is operating at its maximum reactive power limit. The number of non-linear equations required for solving the load flow problem using Newton-Raphson method in polar form is ____________.

A source is supplying a load through a 2-phase, 3-wire transmission system as shown in figure below. The instantaneous voltage and current in phase-a are $$v_{an}=220\sin\left(100\mathrm{πt}\right)\;V$$ and $$i_a=10\sin\left(100\mathrm{πt}\right)\;A$$, respectively. Similarly for phase-b the instantaneous voltage and current are $$v_{bn}=220\cos\left(100\mathrm{πt}\right)\;V$$ and $$i_b=10\cos\left(100\mathrm{πt}\right)\;A$$, respectively. The total instantaneous power flowing form the source to the load is

A load is supplied by a $$230$$ $$V,$$ $$50$$ $$Hz$$ source. The active power $$P$$ and the reactive power $$Q$$ consumed by the load are such that $$1$$ $$kW$$ $$ \le P \le 2\,kW\,\,$$ and $$\,1\,\,kVAR \le 2\,\,kVAR.\,\,$$ A capacitor connected across the load for power factor correction generates $$1$$ $$kVAR$$ reactive power. The worst case power factor after power factor correction is

The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is $$\,1.5\,\,\sin \delta ,\,\,$$ where $$\delta $$ is the rotor angle. The system is operating at the stable equilibrium point with mechanical power equal to $$1$$ pu. If one of the transmission line circuits is removed, the maximum value of $$\delta ,$$ as the rotor swings is $$1.221$$ radian. If the expression for electrical power with one transmission line circuit removed is $$\,{P_{\max }}\,\sin \delta ,\,\,$$ the valueof $${P_{\max }}\,,$$ in pu is _________.